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Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the companys new fleet of jet aircraft and a discount service using smaller-capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based on two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars):

What is the decision to be made, what is the chance event, and what is the consequence for this problem? How many decision alternatives are there? How many outcomes are there for the chance event?
If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?
Suppose that management of Myrtle Air Express believes that the probability of strong demand is 0.7 and the probability of weak demand is 0.3. Use the expected value approach to determine an optimal decision.
Suppose that the probability of strong demand is 0.8 and the probability of weak demand is 0.2. What is the optimal decision using the expected value approach?
Use sensitivity analysis to determine the range of demand probabilities for which each of the decision alternatives has the largest expected value.

## Sample Answer

Decision Analysis for Myrtle Air Express

Introduction

Myrtle Air Express faces an important decision regarding the launch of a new flight service from Cleveland to Myrtle Beach. The management must choose between a full-price service utilizing a new fleet of jet aircraft or a discount service that employs smaller commuter planes. This decision is contingent on the anticipated market demand for the service. Given the estimated quarterly profits for both service models under varying demand scenarios, we will analyze the decision-making process.

Key Concepts

1. Decision to be Made: The primary decision is whether to offer a full-price service with jets or a discount service with commuter planes.

2. Chance Event: The chance event is the level of market demand, which can either be strong or weak.

3. Consequences: The consequences of this decision are reflected in the estimated profits from each service type under different demand levels.

4. Decision Alternatives: There are two decision alternatives:

– Full-price service with jets
– Discount service with commuter planes

5. Outcomes for the Chance Event: There are two possible outcomes for the chance event (demand level):

– Strong demand
– Weak demand

Profit Estimates Table

Service Type Strong Demand ($000) Weak Demand ($000)
Full-price (Jets) 400 100
Discount (Commuter) 250 50

Decision Criteria

Optimistic Approach

Using the optimistic approach, we select the maximum profit for each alternative:

– Full-price (Jets): Maximum profit = $400,000 – Discount (Commuter): Maximum profit =$250,000

Recommended Decision: Full-price service with jets.

Conservative Approach

Using the conservative approach, we select the minimum profit for each alternative:

– Full-price (Jets): Minimum profit = $100,000 – Discount (Commuter): Minimum profit =$50,000

Recommended Decision: Full-price service with jets.

Minimax Regret Approach

1. Calculate regrets for each alternative based on the best outcome in each scenario:

Demand Level Full-price (Jets) Discount (Commuter) Best Outcome Regret (Jets) Regret (Commuter)
Strong Demand 400 250 400 0 150
Weak Demand 100 50 100 0 50

2. Find the maximum regret for each alternative:

– Full-price (Jets): Max Regret = $0 – Discount (Commuter): Max Regret =$150

Recommended Decision: Full-price service with jets.

Expected Value Approach

Assuming probabilities of demand:

1. Probabilities:

– Strong Demand: ( P(S) = 0.7 )
– Weak Demand: ( P(W) = 0.3 )

2. Expected Value Calculation:

[
EV(\text{Full-price}) = (0.7 \times 400) + (0.3 \times 100) = 280 + 30 = 310
]

[
EV(\text{Discount}) = (0.7 \times 250) + (0.3 \times 50) = 175 + 15 = 190
]

Optimal Decision: Full-price service with jets.

Adjusted Probabilities

If the probabilities change to:

– Strong Demand: ( P(S) = 0.8 )
– Weak Demand: ( P(W) = 0.2 )

Recalculating the expected values:

[
EV(\text{Full-price}) = (0.8 \times 400) + (0.2 \times 100) = 320 + 20 = 340
]

[
EV(\text{Discount}) = (0.8 \times 250) + (0.2 \times 50) = 200 + 10 = 210
]

Optimal Decision: Full-price service with jets remains the better option.

Sensitivity Analysis

To determine the range of demand probabilities where each decision alternative has the highest expected value, we set up inequalities based on expected values:

Let ( p ) be the probability of strong demand:

1. For Full-price:
[
EV_{\text{Full-price}} = 400p + 100(1-p) = 300p + 100 &gt; EV_{\text{Discount}}
]
[
300p + 100 &gt; 250p + 50
]
[
50p &gt; -50 \Rightarrow p &gt; \frac{1}{3} \approx 0.33
]

2. For Discount:
[
EV_{\text{Discount}} &gt; EV_{\text{Full-price}}
]
[
250p + 50 &gt; 300p + 100
]
[
-50p &gt; 50 \Rightarrow p &lt; -1 \quad (\text{Not feasible})
]

Conclusion

The analysis indicates that Myrtle Air Express should opt for a full-price service with jets based on all approaches considered, including optimistic, conservative, minimax regret, and expected value analysis. The probability threshold indicates that if strong demand probability is greater than approximately 0.33, the full-price service will yield better expected profits.

This thorough evaluation helps Myrtle Air Express make an informed decision to maximize profitability while mitigating risks associated with demand fluctuations.

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